可信空间上寿险精算的几种生存年金模型

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1、DissertationSubmittedtoHebeiUniversityofTechnologyforTheMasterDegreeofScienceinAppliedMathematicsSOMELIFEANNUITYMODELSOFLIFEACTUARIALONCREDIBILITYSPACEbyZhangYongSupervisor:AssociateProf.XuYongDec.2013万方数据万方数据河北工业大学硕士学位论文摘要在概率空间上的寿险精算模型中，人的生命的不确定性被认定为随机性，进而利用概率测度来度量．然而，人的生命的不确定性是非常复杂的，很难验证其一定满足随机

2、性特征和概率测度下互不相容事件的可列可加性．于是我们尝试把其看作是一种模糊变量，利用模糊测度进行度量．可信测度是刘宝碇教授和刘彦奎教授在2002年给出的一种介于可能性测度和必要性测度两者之间的模糊测度因其满足自对偶性和次可加性，所以在模糊统计中可信测度被认为扮演了类似于概率测度的角色，而且由可信性测度建立的可信性空间也比概率空间更为宽广．本文首先阐述了随机性与模糊性、概率统计与模糊统计、概率空间与可信空间的区别；其次，将寿险中人的余寿看作模糊变量，检验了其满足可信空间上的次可加性；再次，给出了可信性空间上余寿的几种类型及其期望；最后，给出了与余寿相关的几种生存年金的精算现值模型，从而将以

3、上几种生存年金从概率空间推广到可信空间．关键词：可信空间，模糊变量，生存年金，余寿，精算现值I万方数据可信空间上寿险精算的几种生存年金模型ABSTRACTThetraditionalmodelsoflifeactuarialwerefoundedontheprobabilityspace,inwhich,thehumanlife’suncertaintywereassumedasarandomvariablewithprobabilitymeasure.However,theuncertaintyisexceedinglycomplexandthecountableadditivityo

4、fincompatibleeventsunderrandomnessandprobabilitymeasurecannotbeverifiedeasily.Thecontributionofthisthesisisanattemptthatregardstheuncertaintyasafuzzyvariablewithfuzzymeasure.Credibilitymeasuretheoryproposedbyprof.Liu&Liuin2002isakindoffuzzymeasurethatisdefinedbetweenthenecessitymeasureandpossibil

5、itymeasure,andsatisfiesself-dualityandcountablesubadditivity.Therefore,credibilitymeasurecanplayarolesimilartotheprobabilitymeasureinthefuzzystatistics,meanwhile,thecredibilityspacebasedoncredibilitymeasurecandescribemorewideuncertaintyproblemsthanprobabilityspace.Inthisthesis,thedifferencebetwee

6、ntherandomnessandfuzziness,probabilitystatisticsandfuzzystatistics,probabilityspaceandcredibilityspacearediscussedfirstly;Secondly,residuallifeinlifeinsuranceisconsideredasfuzzyvariablesandtheconditionsofsubadditivityoncredibilityspacearedetected;Furthermore,sometypesofresiduallifeandthecorrespon

7、dingexpectationsoncredibilityspaceareproposed;Finally,somelifeactuarialpresentvaluemodelsrelatedtoresiduallifeareproposed,basedonwhich,theabovelifeactuarialcanbeextendedtocredibilityspacefromprobabilityspace.KEYWORDS:c